BAROCLINIC TURBULENCE OF DISSOCIATING GAS

AS A REASON FOR INSTABILITY OF BOW SHOCK

WAVE

A.S.Baryshnikov

Physico-Technical Institute of RAS,

Russia,

The history

• The gases with great molecular weight

is often used for high Much number modeling in free flight of body in ballistic ranges.

One of them is gaseous CF2Cl2 , which has

very high energy of dissociation what is impotent for modeling flight in ideal not reacting gas.

Scheme of ballistic range

Powder gun One of visualization windows with Shlieren set up

receiver

Problem

• When velocity of body riches the amount at which Chemical dissociation (not exothermic reaction) takes the place

• Just a disturbances on bow shock wave are arising.

• The flow behind body becomes disturbed in such manner as for turbulent flow.

• It’s important that such ”turbulence” is outside the wake flow region

Fig.1. Instability of bow shock wave in front of segmental body. Flow Mach number: М0=3,9; Gas: CF2Cl2.

Pressure in flow: Р0=3,8·10 4 Pа.

Wake turbulence

Single vortex

Disturbance on bow shock wave

Fig.2. Instability of bow shock wave in front of segmental body. Flow Mach number: М0=3,9; Gas: CF2Cl2.

Pressure in flow: Р0=4,3·10 4 Pа.

Applications

• Reducing a drag of air vehicles (destabilization and destruction of bow shock wave),

At dropping of Temperature and so of heat flux to surface!!!

• Controlling a flight of them,

• Without any energy deposition (Compare with case of plasma control),

Usual study region

Fig.3. Estimation of one dimension spectrum of density fluctuations in investigated region of turbulent flow behind

segmental body higher than axis. Body diameter d=27 mm, CF2Cl2; М0=6,8 , Р0=3,8·104Pа, length of realizations

Θ =18 mm.I(ξ) Db

ξ bin

-20

-40

100 200

ξ is normalized wave number of fluctuations

Fig.4. Estimation of one dimension spectrum of density fluctuations in investigated region of turbulent flow behind sphere body higher and

lower than axis. Body diameter d=27 mm, CF2Cl2; М0=6,1 , Р0=8·104Pа, length of realizations Θ =41 mm.

I(ξ) Db

15010050

-10

-20

-30

-40

200 ξ bin

Estimation of energy spectra

• For isotropy turbulence we have

)(2)( 2 IE

Fig.5. Estimation of three dimension energy spectrum of turbulence in investigated flow region behind segmental body higher than axis. Body diameter d=27 mm, CF2Cl2; М0=6,8, Р0=3,8·104Pа, length of realizations Θ =18 mm.

max

2 )(

I

I

1/rc

Fig.6. Estimation of three dimension energy spectrum of turbulence in investigated flow region behind sphere body higher and lower than

axis. Body diameter d=27 мм, CF2Cl2; М0=6,1, Р0=8·104Па, Θ =41 mm.

max

2 )(

I

I

1/rc

Some conclusions from spectral estimations

• Maximum amount of three dimensional spectrum in the investigated region of waves numbers

(Fig.5-6) corresponds to vortexes with character size 2rc θ ξmax , rc ≈ 0,3 mm (θ - length of realization, ξmax -wave number corresponds to maximum of spectra intercity)

• This size is local dimension of investigated turbulence. It can be used for obtaining estimations of energy of turbulent pulses near 100 kDj/kg [experiment].

• As it will be shown this energy is well compared with character energy of physical-chemical processes determining the turbulence pulses 90,8 kDj/kg

• which is the energy of dissociation of molecule of CF2Cl2.

• The baroclinic term is conditioned by change the entropy - grad S

How to explaine the turbulence arising?

Let’s write equation for vorticety Ω

= B

Estimation of energy amount conditioned the flow instability

• For this aim the relation connected entropy changing, -ΔS, with a vortices in gas particle in

homogeneous stationary flow. • The amount of energy participated in thermal exchange, - q, for chemical processes is simply

the same as T·S. • Stationary equation of fluid dynamics will be:

•

V

Vrot

][ qgradSgradT

This situation is just realized for 1. large Damkeler number ratio of reacting time to the time of flow ( so called almost

frozen flow) and 2. for such polyatomic gas as CF2Cl2 with

high energy of dissociation

Deposition of chemical processes in change of entropy ΔS for

great dissociation energy ΔH, little concentration lnζk and great grad ζ k of

products becomes very large:

∆Hk, Mk, ζk – creation energy, molecular weight and concentration of spesies; RΓ - gas constant

k

kkkkk MRMHS )]1)(ln/()/[(

Use the model of rolling swirl

V

r

VVrot 2

r

V 2

2Vrot

∆q = x

m

r

VV 126 102

kg

kDj

Here is Vm ≈ 250 - the middle flow velocity near the lateral surface m/s. [ found from estimation of full mass

consumption of gas stream (≈ 3,4 kg/s) between the shock wave and lateral surface].

∆S = almost

(consider that vortex of characteristic size r is moving along the surface as if it is rolling along the surface

without slide)

The second step in turbulence investigation, which could give the answer for a question about a nature of phenomena, could be made,

consider the dissipation function:

• )()( 2 ED

Maximum of it corresponds to dimension of vortexes, on which main part of pulses energy in gas is

dissipated

•energy diffusion due to the dissipation take the place if their dimension about of order of amount or larger than

Kolmogorov's micro dimension of turbulence:

• )/( 3x

•εx - mass density of power of dissipation,

• ν - the viscosity of gas

Table 1.Table 1. η - Kolmogorov's microdimension. ηη - Kolmogorov's microdimension. ηdd - Dimension of vortexes - Dimension of vortexes

which is most intensely dissipated ξwhich is most intensely dissipated ξdd - amount of wave number at - amount of wave number at

which dissipation function have an absolute maximum, ε - mass density which dissipation function have an absolute maximum, ε - mass density of power of dissipation.of power of dissipation.

ηηd

m

ηη

m

ξd

bin

ε W/kg

Usual viscose stationary turbulence (estimation)

6

10-5 6

10-6

7

102

2

107

Estimation found from experimental data and data of energy release at dissociation

1

10-6 1 10-7

4 104

5

1010

Estimation from equilibrium energy of oscillatory degrees of freedom.

2

10-6 2

10-7

2 104

7

109

Some conclusions

• estimation of power of dissipation of investigated turbulent flow (second row)

• is close and almost higher than• estimation made for the case of release of all

equilibrium energy of oscillatory degrees of freedom third row (accuracy of ε in frames of order of value).

• Then its amount is greater than estimation for usual viscose stationary turbulence in three orders of value.

So

• appearance of turbulent flow in experiments is not conditioned by viscose dissipation of flow energy on the lateral surface

• and is connected with excitation of more energy capable degrees of freedom than oscillatory one.

• Such degrees of freedom can be, for instance,

the chemical degrees or degrees of electron excitation.

Fig.8. Scheme of flow around blunt body at the “transformation to reacting” regime.

Dashed region is high entropy layer of gas flow.

grad S is not coincides with vector of V, so rotV is not zero

Reactions are only at stagnation point and products flow near the surface of body

• The gradient is conditioned by difference of entropy between its value on surface and on shock wave – ΔS,

• and by the depart of shock wave from surface - δ. • Assume once more the following model of rolling

swirl:• let's consider that vortex of characteristic size

is moving along the surface as if it is rolling along the surface without slide

• alike cylinder of radius – r(t). • Then:

Vrot

=2V/r r

VST

22

1. Interaction of vortex with shock wave takes the place if

r≥0,5δ; i.e. at

STV 24

2. On the other hand for perturbation of shock wave it's necessary that V≤Vsound

2/1

*

RT 2/12

2

14 STV

γ* , μ – effective ratio of specific thermo capacities of gas and its molecular weight in compression zone

Two conditions take the place if:

R*

4S

•this criteria is valid•for regime at which first (at shock wave Mach number arising) disturbances on shock wave were observed at

flow of CF2Cl2 around the blunt body.

•( M∞=4, P∞=0,04 MPa )

•INDEED:

Temperature and pressure in critical point will be: T=750 K, P=0,1 MPa

There is experimental data of equilibrium chemical composition of dissociation of CF2Cl2 about at this

temperature and pressure:

• Trenwith A.B., Watson R.H. Thermal decomposition of chlorofluoromethanes.// J.Chem.Soc. (London). 1957. N 5. P.2368-2372

• Using it we can find T∆S=90,8 kDj/kg. • Then (ТS)=150,7 m/s. • Since sound speed in CF2Cl2 at this regimes 239 m/s (at

γ* ≈1,1) criterion (14) take the place. • At rising of M∞ and P∞ they reach the values at which

criterion (14) is not available (for instance for P∞=0,04 MPa it is M∞=6)

• and center of disturbances creation is moving from region of lateral flow to region of bottom flow.

Comparison with experiment

• In experiments we observe that perturbations of shock wave front (and of the flow behind it) indeed

• at P∞=0,04 MPa at M∞=4 is of find scale 0.3 mm

• But at M∞=6 they are almost neglected.

•

Summary

• We can say from experimental study and made estimations

• that effect of so called instability of bow shock wave and flow behind it

• Is conditioned by the baroclinic type of flow of reacting gas in compression zone between bow shock

wave and bow surface • I am very thanks for collaboration first of all to A.Bedin,

then to V.Derevyanko, V.Maslennikov, I.Basargin and M.Chistyakova.

Thank you for attention